Actual source code: glee.c

  1: /*
  2:   Code for time stepping with the General Linear with Error Estimation method

  4:   Notes:
  5:   The general system is written as

  7:   Udot = F(t,U)

  9: */
 10: #include <petsc/private/tsimpl.h>
 11: #include <petscdm.h>

 13: static PetscBool  cited      = PETSC_FALSE;
 14: static const char citation[] = "@ARTICLE{Constantinescu_TR2016b,\n"
 15:                                " author = {Constantinescu, E.M.},\n"
 16:                                " title = {Estimating Global Errors in Time Stepping},\n"
 17:                                " journal = {ArXiv e-prints},\n"
 18:                                " year = 2016,\n"
 19:                                " adsurl = {http://adsabs.harvard.edu/abs/2015arXiv150305166C}\n}\n";

 21: static TSGLEEType TSGLEEDefaultType = TSGLEE35;
 22: static PetscBool  TSGLEERegisterAllCalled;
 23: static PetscBool  TSGLEEPackageInitialized;
 24: static PetscInt   explicit_stage_time_id;

 26: typedef struct _GLEETableau *GLEETableau;
 27: struct _GLEETableau {
 28:   char      *name;
 29:   PetscInt   order;                     /* Classical approximation order of the method i*/
 30:   PetscInt   s;                         /* Number of stages */
 31:   PetscInt   r;                         /* Number of steps */
 32:   PetscReal  gamma;                     /* LTE ratio */
 33:   PetscReal *A, *B, *U, *V, *S, *F, *c; /* Tableau */
 34:   PetscReal *Fembed;                    /* Embedded final method coefficients */
 35:   PetscReal *Ferror;                    /* Coefficients for computing error   */
 36:   PetscReal *Serror;                    /* Coefficients for initializing the error   */
 37:   PetscInt   pinterp;                   /* Interpolation order */
 38:   PetscReal *binterp;                   /* Interpolation coefficients */
 39:   PetscReal  ccfl;                      /* Placeholder for CFL coefficient relative to forward Euler  */
 40: };
 41: typedef struct _GLEETableauLink *GLEETableauLink;
 42: struct _GLEETableauLink {
 43:   struct _GLEETableau tab;
 44:   GLEETableauLink     next;
 45: };
 46: static GLEETableauLink GLEETableauList;

 48: typedef struct {
 49:   GLEETableau  tableau;
 50:   Vec         *Y;         /* Solution vector (along with auxiliary solution y~ or eps) */
 51:   Vec         *X;         /* Temporary solution vector */
 52:   Vec         *YStage;    /* Stage values */
 53:   Vec         *YdotStage; /* Stage right-hand side */
 54:   Vec          W;         /* Right-hand-side for implicit stage solve */
 55:   Vec          Ydot;      /* Work vector holding Ydot during residual evaluation */
 56:   Vec          yGErr;     /* Vector holding the global error after a step is completed */
 57:   PetscScalar *swork;     /* Scalar work (size of the number of stages)*/
 58:   PetscScalar *rwork;     /* Scalar work (size of the number of steps)*/
 59:   PetscReal    scoeff;    /* shift = scoeff/dt */
 60:   PetscReal    stage_time;
 61:   TSStepStatus status;
 62: } TS_GLEE;

 64: /*MC
 65:      TSGLEE23 - Second order three stage GLEE method

 67:      This method has three stages.
 68:      s = 3, r = 2

 70:      Level: advanced

 72: .seealso: [](ch_ts), `TSGLEE`
 73: M*/
 74: /*MC
 75:      TSGLEE24 - Second order four stage GLEE method

 77:      This method has four stages.
 78:      s = 4, r = 2

 80:      Level: advanced

 82: .seealso: [](ch_ts), `TSGLEE`
 83: M*/
 84: /*MC
 85:      TSGLEE25i - Second order five stage GLEE method

 87:      This method has five stages.
 88:      s = 5, r = 2

 90:      Level: advanced

 92: .seealso: [](ch_ts), `TSGLEE`
 93: M*/
 94: /*MC
 95:      TSGLEE35  - Third order five stage GLEE method

 97:      This method has five stages.
 98:      s = 5, r = 2

100:      Level: advanced

102: .seealso: [](ch_ts), `TSGLEE`
103: M*/
104: /*MC
105:      TSGLEEEXRK2A  - Second order six stage GLEE method

107:      This method has six stages.
108:      s = 6, r = 2

110:      Level: advanced

112: .seealso: [](ch_ts), `TSGLEE`
113: M*/
114: /*MC
115:      TSGLEERK32G1  - Third order eight stage GLEE method

117:      This method has eight stages.
118:      s = 8, r = 2

120:      Level: advanced

122: .seealso: [](ch_ts), `TSGLEE`
123: M*/
124: /*MC
125:      TSGLEERK285EX  - Second order nine stage GLEE method

127:      This method has nine stages.
128:      s = 9, r = 2

130:      Level: advanced

132: .seealso: [](ch_ts), `TSGLEE`
133: M*/

135: /*@C
136:   TSGLEERegisterAll - Registers all of the General Linear with Error Estimation methods in `TSGLEE`

138:   Not Collective, but should be called by all processes which will need the schemes to be registered

140:   Level: advanced

142: .seealso: [](ch_ts), `TSGLEERegisterDestroy()`
143: @*/
144: PetscErrorCode TSGLEERegisterAll(void)
145: {
146:   PetscFunctionBegin;
147:   if (TSGLEERegisterAllCalled) PetscFunctionReturn(PETSC_SUCCESS);
148:   TSGLEERegisterAllCalled = PETSC_TRUE;

150:   {
151: #define GAMMA 0.5
152:     /* y-eps form */
153:     const PetscInt  p = 1, s = 3, r = 2;
154:     const PetscReal A[3][3] =
155:       {
156:         {1.0, 0,   0  },
157:         {0,   0.5, 0  },
158:         {0,   0.5, 0.5}
159:     },
160:                     B[2][3] = {{1.0, 0, 0}, {-2.0, 1.0, 1.0}}, U[3][2] = {{1.0, 0}, {1.0, 0.5}, {1.0, 0.5}}, V[2][2] = {{1, 0}, {0, 1}}, S[2] = {1, 0}, F[2] = {1, 0}, Fembed[2] = {1, 1 - GAMMA}, Ferror[2] = {0, 1}, Serror[2] = {1, 0};
161:     PetscCall(TSGLEERegister(TSGLEEi1, p, s, r, GAMMA, &A[0][0], &B[0][0], &U[0][0], &V[0][0], S, F, NULL, Fembed, Ferror, Serror, 0, NULL));
162:   }
163:   {
164: #undef GAMMA
165: #define GAMMA 0.0
166:     /* y-eps form */
167:     const PetscInt  p = 2, s = 3, r = 2;
168:     const PetscReal A[3][3] =
169:       {
170:         {0,    0,    0},
171:         {1,    0,    0},
172:         {0.25, 0.25, 0}
173:     },
174:                     B[2][3] = {{1.0 / 12.0, 1.0 / 12.0, 5.0 / 6.0}, {1.0 / 12.0, 1.0 / 12.0, -1.0 / 6.0}}, U[3][2] = {{1, 0}, {1, 10}, {1, -1}}, V[2][2] = {{1, 0}, {0, 1}}, S[2] = {1, 0}, F[2] = {1, 0}, Fembed[2] = {1, 1 - GAMMA}, Ferror[2] = {0, 1}, Serror[2] = {1, 0};
175:     PetscCall(TSGLEERegister(TSGLEE23, p, s, r, GAMMA, &A[0][0], &B[0][0], &U[0][0], &V[0][0], S, F, NULL, Fembed, Ferror, Serror, 0, NULL));
176:   }
177:   {
178: #undef GAMMA
179: #define GAMMA 0.0
180:     /* y-y~ form */
181:     const PetscInt  p = 2, s = 4, r = 2;
182:     const PetscReal A[4][4] =
183:       {
184:         {0,            0,            0,            0},
185:         {0.75,         0,            0,            0},
186:         {0.25,         29.0 / 60.0,  0,            0},
187:         {-21.0 / 44.0, 145.0 / 44.0, -20.0 / 11.0, 0}
188:     },
189:                     B[2][4] = {{109.0 / 275.0, 58.0 / 75.0, -37.0 / 110.0, 1.0 / 6.0}, {3.0 / 11.0, 0, 75.0 / 88.0, -1.0 / 8.0}}, U[4][2] = {{0, 1}, {75.0 / 58.0, -17.0 / 58.0}, {0, 1}, {0, 1}}, V[2][2] = {{1, 0}, {0, 1}}, S[2] = {1, 1}, F[2] = {1, 0}, Fembed[2] = {0, 1}, Ferror[2] = {-1.0 / (1.0 - GAMMA), 1.0 / (1.0 - GAMMA)}, Serror[2] = {1.0 - GAMMA, 1.0};
190:     PetscCall(TSGLEERegister(TSGLEE24, p, s, r, GAMMA, &A[0][0], &B[0][0], &U[0][0], &V[0][0], S, F, NULL, Fembed, Ferror, Serror, 0, NULL));
191:   }
192:   {
193: #undef GAMMA
194: #define GAMMA 0.0
195:     /* y-y~ form */
196:     const PetscInt  p = 2, s = 5, r = 2;
197:     const PetscReal A[5][5] =
198:       {
199:         {0,                       0,                       0,                       0,                      0},
200:         {-0.94079244066783383269, 0,                       0,                       0,                      0},
201:         {0.64228187778301907108,  0.10915356933958500042,  0,                       0,                      0},
202:         {-0.51764297742287450812, 0.74414270351096040738,  -0.71404164927824538121, 0,                      0},
203:         {-0.44696561556825969206, -0.76768425657590196518, 0.20111608138142987881,  0.93828186737840469796, 0}
204:     },
205:                     B[2][5] = {{-0.029309178948150356153, -0.49671981884013874923, 0.34275801517650053274, 0.32941112623949194988, 0.85385985637229662276}, {0.78133219686062535272, 0.074238691892675897635, 0.57957363498384957966, -0.24638502829674959968, -0.18875949544040123033}}, U[5][2] = {{0.16911424754448327735, 0.83088575245551672265}, {0.53638465733199574340, 0.46361534266800425660}, {0.39901579167169582526, 0.60098420832830417474}, {0.87689005530618575480, 0.12310994469381424520}, {0.99056100455550913009, 0.0094389954444908699092}}, V[2][2] = {{1, 0}, {0, 1}}, S[2] = {1, 1}, F[2] = {1, 0}, Fembed[2] = {0, 1}, Ferror[2] = {-1.0 / (1.0 - GAMMA), 1.0 / (1.0 - GAMMA)}, Serror[2] = {1.0 - GAMMA, 1.0};
206:     PetscCall(TSGLEERegister(TSGLEE25I, p, s, r, GAMMA, &A[0][0], &B[0][0], &U[0][0], &V[0][0], S, F, NULL, Fembed, Ferror, Serror, 0, NULL));
207:   }
208:   {
209: #undef GAMMA
210: #define GAMMA 0.0
211:     /* y-y~ form */
212:     const PetscInt  p = 3, s = 5, r = 2;
213:     const PetscReal A[5][5] =
214:       {
215:         {0,                                                0,                                                 0,                                                 0,                                               0},
216:         {-2169604947363702313.0 / 24313474998937147335.0,  0,                                                 0,                                                 0,                                               0},
217:         {46526746497697123895.0 / 94116917485856474137.0,  -10297879244026594958.0 / 49199457603717988219.0,  0,                                                 0,                                               0},
218:         {23364788935845982499.0 / 87425311444725389446.0,  -79205144337496116638.0 / 148994349441340815519.0, 40051189859317443782.0 / 36487615018004984309.0,   0,                                               0},
219:         {42089522664062539205.0 / 124911313006412840286.0, -15074384760342762939.0 / 137927286865289746282.0, -62274678522253371016.0 / 125918573676298591413.0, 13755475729852471739.0 / 79257927066651693390.0, 0}
220:     },
221:                     B[2][5] = {{61546696837458703723.0 / 56982519523786160813.0, -55810892792806293355.0 / 206957624151308356511.0, 24061048952676379087.0 / 158739347956038723465.0, 3577972206874351339.0 / 7599733370677197135.0, -59449832954780563947.0 / 137360038685338563670.0}, {-9738262186984159168.0 / 99299082461487742983.0, -32797097931948613195.0 / 61521565616362163366.0, 42895514606418420631.0 / 71714201188501437336.0, 22608567633166065068.0 / 55371917805607957003.0, 94655809487476459565.0 / 151517167160302729021.0}}, U[5][2] = {{70820309139834661559.0 / 80863923579509469826.0, 10043614439674808267.0 / 80863923579509469826.0}, {161694774978034105510.0 / 106187653640211060371.0, -55507121337823045139.0 / 106187653640211060371.0}, {78486094644566264568.0 / 88171030896733822981.0, 9684936252167558413.0 / 88171030896733822981.0}, {65394922146334854435.0 / 84570853840405479554.0, 19175931694070625119.0 / 84570853840405479554.0}, {8607282770183754108.0 / 108658046436496925911.0, 100050763666313171803.0 / 108658046436496925911.0}}, V[2][2] = {{1, 0}, {0, 1}}, S[2] = {1, 1}, F[2] = {1, 0}, Fembed[2] = {0, 1}, Ferror[2] = {-1.0 / (1.0 - GAMMA), 1.0 / (1.0 - GAMMA)}, Serror[2] = {1.0 - GAMMA, 1.0};
222:     PetscCall(TSGLEERegister(TSGLEE35, p, s, r, GAMMA, &A[0][0], &B[0][0], &U[0][0], &V[0][0], S, F, NULL, Fembed, Ferror, Serror, 0, NULL));
223:   }
224:   {
225: #undef GAMMA
226: #define GAMMA 0.25
227:     /* y-eps form */
228:     const PetscInt  p = 2, s = 6, r = 2;
229:     const PetscReal A[6][6] =
230:       {
231:         {0, 0, 0,    0,    0,   0},
232:         {1, 0, 0,    0,    0,   0},
233:         {0, 0, 0,    0,    0,   0},
234:         {0, 0, 0.5,  0,    0,   0},
235:         {0, 0, 0.25, 0.25, 0,   0},
236:         {0, 0, 0.25, 0.25, 0.5, 0}
237:     },
238:                     B[2][6] = {{0.5, 0.5, 0, 0, 0, 0}, {-2.0 / 3.0, -2.0 / 3.0, 1.0 / 3.0, 1.0 / 3.0, 1.0 / 3.0, 1.0 / 3.0}}, U[6][2] = {{1, 0}, {1, 0}, {1, 0.75}, {1, 0.75}, {1, 0.75}, {1, 0.75}}, V[2][2] = {{1, 0}, {0, 1}}, S[2] = {1, 0}, F[2] = {1, 0}, Fembed[2] = {1, 1 - GAMMA}, Ferror[2] = {0, 1}, Serror[2] = {1, 0};
239:     PetscCall(TSGLEERegister(TSGLEEEXRK2A, p, s, r, GAMMA, &A[0][0], &B[0][0], &U[0][0], &V[0][0], S, F, NULL, Fembed, Ferror, Serror, 0, NULL));
240:   }
241:   {
242: #undef GAMMA
243: #define GAMMA 0.0
244:     /* y-eps form */
245:     const PetscInt  p = 3, s = 8, r = 2;
246:     const PetscReal A[8][8] =
247:       {
248:         {0,           0,          0,          0,          0,         0,         0,         0},
249:         {0.5,         0,          0,          0,          0,         0,         0,         0},
250:         {-1,          2,          0,          0,          0,         0,         0,         0},
251:         {1.0 / 6.0,   2.0 / 3.0,  1.0 / 6.0,  0,          0,         0,         0,         0},
252:         {0,           0,          0,          0,          0,         0,         0,         0},
253:         {-7.0 / 24.0, 1.0 / 3.0,  1.0 / 12.0, -1.0 / 8.0, 0.5,       0,         0,         0},
254:         {7.0 / 6.0,   -4.0 / 3.0, -1.0 / 3.0, 0.5,        -1.0,      2.0,       0,         0},
255:         {0,           0,          0,          0,          1.0 / 6.0, 2.0 / 3.0, 1.0 / 6.0, 0}
256:     },
257:                     B[2][8] = {{1.0 / 6.0, 2.0 / 3.0, 1.0 / 6.0, 0, 0, 0, 0, 0}, {-1.0 / 6.0, -2.0 / 3.0, -1.0 / 6.0, 0, 1.0 / 6.0, 2.0 / 3.0, 1.0 / 6.0, 0}}, U[8][2] = {{1, 0}, {1, 0}, {1, 0}, {1, 0}, {1, 1}, {1, 1}, {1, 1}, {1, 1}}, V[2][2] = {{1, 0}, {0, 1}}, S[2] = {1, 0}, F[2] = {1, 0}, Fembed[2] = {1, 1 - GAMMA}, Ferror[2] = {0, 1}, Serror[2] = {1, 0};
258:     PetscCall(TSGLEERegister(TSGLEERK32G1, p, s, r, GAMMA, &A[0][0], &B[0][0], &U[0][0], &V[0][0], S, F, NULL, Fembed, Ferror, Serror, 0, NULL));
259:   }
260:   {
261: #undef GAMMA
262: #define GAMMA 0.25
263:     /* y-eps form */
264:     const PetscInt  p = 2, s = 9, r = 2;
265:     const PetscReal A[9][9] =
266:       {
267:         {0,                    0,                    0, 0,                     0,                    0,                    0,                     0,                    0},
268:         {0.585786437626904966, 0,                    0, 0,                     0,                    0,                    0,                     0,                    0},
269:         {0.149999999999999994, 0.849999999999999978, 0, 0,                     0,                    0,                    0,                     0,                    0},
270:         {0,                    0,                    0, 0,                     0,                    0,                    0,                     0,                    0},
271:         {0,                    0,                    0, 0.292893218813452483,  0,                    0,                    0,                     0,                    0},
272:         {0,                    0,                    0, 0.0749999999999999972, 0.424999999999999989, 0,                    0,                     0,                    0},
273:         {0,                    0,                    0, 0.176776695296636893,  0.176776695296636893, 0.146446609406726241, 0,                     0,                    0},
274:         {0,                    0,                    0, 0.176776695296636893,  0.176776695296636893, 0.146446609406726241, 0.292893218813452483,  0,                    0},
275:         {0,                    0,                    0, 0.176776695296636893,  0.176776695296636893, 0.146446609406726241, 0.0749999999999999972, 0.424999999999999989, 0}
276:     },
277:                     B[2][9] = {{0.353553390593273786, 0.353553390593273786, 0.292893218813452483, 0, 0, 0, 0, 0, 0}, {-0.471404520791031678, -0.471404520791031678, -0.390524291751269959, 0.235702260395515839, 0.235702260395515839, 0.195262145875634979, 0.235702260395515839, 0.235702260395515839, 0.195262145875634979}}, U[9][2] = {{1, 0}, {1, 0}, {1, 0}, {1, 0.75}, {1, 0.75}, {1, 0.75}, {1, 0.75}, {1, 0.75}, {1, 0.75}}, V[2][2] = {{1, 0}, {0, 1}}, S[2] = {1, 0}, F[2] = {1, 0}, Fembed[2] = {1, 1 - GAMMA}, Ferror[2] = {0, 1}, Serror[2] = {1, 0};
278:     PetscCall(TSGLEERegister(TSGLEERK285EX, p, s, r, GAMMA, &A[0][0], &B[0][0], &U[0][0], &V[0][0], S, F, NULL, Fembed, Ferror, Serror, 0, NULL));
279:   }
280:   PetscFunctionReturn(PETSC_SUCCESS);
281: }

283: /*@C
284:   TSGLEERegisterDestroy - Frees the list of schemes that were registered by `TSGLEERegister()`.

286:   Not Collective

288:   Level: advanced

290: .seealso: [](ch_ts), `TSGLEERegister()`, `TSGLEERegisterAll()`
291: @*/
292: PetscErrorCode TSGLEERegisterDestroy(void)
293: {
294:   GLEETableauLink link;

296:   PetscFunctionBegin;
297:   while ((link = GLEETableauList)) {
298:     GLEETableau t   = &link->tab;
299:     GLEETableauList = link->next;
300:     PetscCall(PetscFree5(t->A, t->B, t->U, t->V, t->c));
301:     PetscCall(PetscFree2(t->S, t->F));
302:     PetscCall(PetscFree(t->Fembed));
303:     PetscCall(PetscFree(t->Ferror));
304:     PetscCall(PetscFree(t->Serror));
305:     PetscCall(PetscFree(t->binterp));
306:     PetscCall(PetscFree(t->name));
307:     PetscCall(PetscFree(link));
308:   }
309:   TSGLEERegisterAllCalled = PETSC_FALSE;
310:   PetscFunctionReturn(PETSC_SUCCESS);
311: }

313: /*@C
314:   TSGLEEInitializePackage - This function initializes everything in the `TSGLEE` package. It is called
315:   from `TSInitializePackage()`.

317:   Level: developer

319: .seealso: [](ch_ts), `PetscInitialize()`
320: @*/
321: PetscErrorCode TSGLEEInitializePackage(void)
322: {
323:   PetscFunctionBegin;
324:   if (TSGLEEPackageInitialized) PetscFunctionReturn(PETSC_SUCCESS);
325:   TSGLEEPackageInitialized = PETSC_TRUE;
326:   PetscCall(TSGLEERegisterAll());
327:   PetscCall(PetscObjectComposedDataRegister(&explicit_stage_time_id));
328:   PetscCall(PetscRegisterFinalize(TSGLEEFinalizePackage));
329:   PetscFunctionReturn(PETSC_SUCCESS);
330: }

332: /*@C
333:   TSGLEEFinalizePackage - This function destroys everything in the `TSGLEE` package. It is
334:   called from `PetscFinalize()`.

336:   Level: developer

338: .seealso: [](ch_ts), `PetscFinalize()`
339: @*/
340: PetscErrorCode TSGLEEFinalizePackage(void)
341: {
342:   PetscFunctionBegin;
343:   TSGLEEPackageInitialized = PETSC_FALSE;
344:   PetscCall(TSGLEERegisterDestroy());
345:   PetscFunctionReturn(PETSC_SUCCESS);
346: }

348: /*@C
349:   TSGLEERegister - register a new `TSGLEE` scheme by providing the entries in the Butcher tableau

351:   Not Collective, but the same schemes should be registered on all processes on which they will be used

353:   Input Parameters:
354: + name    - identifier for method
355: . order   - order of method
356: . s       - number of stages
357: . r       - number of steps
358: . gamma   - LTE ratio
359: . A       - stage coefficients (dimension s*s, row-major)
360: . B       - step completion coefficients (dimension r*s, row-major)
361: . U       - method coefficients (dimension s*r, row-major)
362: . V       - method coefficients (dimension r*r, row-major)
363: . S       - starting coefficients
364: . F       - finishing coefficients
365: . c       - abscissa (dimension s; NULL to use row sums of A)
366: . Fembed  - step completion coefficients for embedded method
367: . Ferror  - error computation coefficients
368: . Serror  - error initialization coefficients
369: . pinterp - order of interpolation (0 if unavailable)
370: - binterp - array of interpolation coefficients (NULL if unavailable)

372:   Level: advanced

374:   Note:
375:   Several `TSGLEE` methods are provided, this function is only needed to create new methods.

377: .seealso: [](ch_ts), `TSGLEE`
378: @*/
379: PetscErrorCode TSGLEERegister(TSGLEEType name, PetscInt order, PetscInt s, PetscInt r, PetscReal gamma, const PetscReal A[], const PetscReal B[], const PetscReal U[], const PetscReal V[], const PetscReal S[], const PetscReal F[], const PetscReal c[], const PetscReal Fembed[], const PetscReal Ferror[], const PetscReal Serror[], PetscInt pinterp, const PetscReal binterp[])
380: {
381:   GLEETableauLink link;
382:   GLEETableau     t;
383:   PetscInt        i, j;

385:   PetscFunctionBegin;
386:   PetscCall(TSGLEEInitializePackage());
387:   PetscCall(PetscNew(&link));
388:   t = &link->tab;
389:   PetscCall(PetscStrallocpy(name, &t->name));
390:   t->order = order;
391:   t->s     = s;
392:   t->r     = r;
393:   t->gamma = gamma;
394:   PetscCall(PetscMalloc5(s * s, &t->A, r * r, &t->V, s, &t->c, r * s, &t->B, s * r, &t->U));
395:   PetscCall(PetscMalloc2(r, &t->S, r, &t->F));
396:   PetscCall(PetscArraycpy(t->A, A, s * s));
397:   PetscCall(PetscArraycpy(t->B, B, r * s));
398:   PetscCall(PetscArraycpy(t->U, U, s * r));
399:   PetscCall(PetscArraycpy(t->V, V, r * r));
400:   PetscCall(PetscArraycpy(t->S, S, r));
401:   PetscCall(PetscArraycpy(t->F, F, r));
402:   if (c) {
403:     PetscCall(PetscArraycpy(t->c, c, s));
404:   } else {
405:     for (i = 0; i < s; i++)
406:       for (j = 0, t->c[i] = 0; j < s; j++) t->c[i] += A[i * s + j];
407:   }
408:   PetscCall(PetscMalloc1(r, &t->Fembed));
409:   PetscCall(PetscMalloc1(r, &t->Ferror));
410:   PetscCall(PetscMalloc1(r, &t->Serror));
411:   PetscCall(PetscArraycpy(t->Fembed, Fembed, r));
412:   PetscCall(PetscArraycpy(t->Ferror, Ferror, r));
413:   PetscCall(PetscArraycpy(t->Serror, Serror, r));
414:   t->pinterp = pinterp;
415:   PetscCall(PetscMalloc1(s * pinterp, &t->binterp));
416:   PetscCall(PetscArraycpy(t->binterp, binterp, s * pinterp));

418:   link->next      = GLEETableauList;
419:   GLEETableauList = link;
420:   PetscFunctionReturn(PETSC_SUCCESS);
421: }

423: static PetscErrorCode TSEvaluateStep_GLEE(TS ts, PetscInt order, Vec X, PetscBool *done)
424: {
425:   TS_GLEE     *glee = (TS_GLEE *)ts->data;
426:   GLEETableau  tab  = glee->tableau;
427:   PetscReal    h, *B = tab->B, *V = tab->V, *F = tab->F, *Fembed = tab->Fembed;
428:   PetscInt     s = tab->s, r = tab->r, i, j;
429:   Vec         *Y = glee->Y, *YdotStage = glee->YdotStage;
430:   PetscScalar *ws = glee->swork, *wr = glee->rwork;

432:   PetscFunctionBegin;
433:   switch (glee->status) {
434:   case TS_STEP_INCOMPLETE:
435:   case TS_STEP_PENDING:
436:     h = ts->time_step;
437:     break;
438:   case TS_STEP_COMPLETE:
439:     h = ts->ptime - ts->ptime_prev;
440:     break;
441:   default:
442:     SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_PLIB, "Invalid TSStepStatus");
443:   }

445:   if (order == tab->order) {
446:     /* Note: Irrespective of whether status is TS_STEP_INCOMPLETE
447:              or TS_STEP_COMPLETE, glee->X has the solution at the
448:              beginning of the time step. So no need to roll-back.
449:     */
450:     if (glee->status == TS_STEP_INCOMPLETE) {
451:       for (i = 0; i < r; i++) {
452:         PetscCall(VecZeroEntries(Y[i]));
453:         for (j = 0; j < r; j++) wr[j] = V[i * r + j];
454:         PetscCall(VecMAXPY(Y[i], r, wr, glee->X));
455:         for (j = 0; j < s; j++) ws[j] = h * B[i * s + j];
456:         PetscCall(VecMAXPY(Y[i], s, ws, YdotStage));
457:       }
458:       PetscCall(VecZeroEntries(X));
459:       for (j = 0; j < r; j++) wr[j] = F[j];
460:       PetscCall(VecMAXPY(X, r, wr, Y));
461:     } else PetscCall(VecCopy(ts->vec_sol, X));
462:     PetscFunctionReturn(PETSC_SUCCESS);

464:   } else if (order == tab->order - 1) {
465:     /* Complete with the embedded method (Fembed) */
466:     for (i = 0; i < r; i++) {
467:       PetscCall(VecZeroEntries(Y[i]));
468:       for (j = 0; j < r; j++) wr[j] = V[i * r + j];
469:       PetscCall(VecMAXPY(Y[i], r, wr, glee->X));
470:       for (j = 0; j < s; j++) ws[j] = h * B[i * s + j];
471:       PetscCall(VecMAXPY(Y[i], s, ws, YdotStage));
472:     }
473:     PetscCall(VecZeroEntries(X));
474:     for (j = 0; j < r; j++) wr[j] = Fembed[j];
475:     PetscCall(VecMAXPY(X, r, wr, Y));

477:     if (done) *done = PETSC_TRUE;
478:     PetscFunctionReturn(PETSC_SUCCESS);
479:   }
480:   if (done) *done = PETSC_FALSE;
481:   else SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "GLEE '%s' of order %" PetscInt_FMT " cannot evaluate step at order %" PetscInt_FMT, tab->name, tab->order, order);
482:   PetscFunctionReturn(PETSC_SUCCESS);
483: }

485: static PetscErrorCode TSStep_GLEE(TS ts)
486: {
487:   TS_GLEE       *glee = (TS_GLEE *)ts->data;
488:   GLEETableau    tab  = glee->tableau;
489:   const PetscInt s = tab->s, r = tab->r;
490:   PetscReal     *A = tab->A, *U = tab->U, *F = tab->F, *c = tab->c;
491:   Vec           *Y = glee->Y, *X = glee->X, *YStage = glee->YStage, *YdotStage = glee->YdotStage, W = glee->W;
492:   SNES           snes;
493:   PetscScalar   *ws = glee->swork, *wr = glee->rwork;
494:   TSAdapt        adapt;
495:   PetscInt       i, j, reject, next_scheme, its, lits;
496:   PetscReal      next_time_step;
497:   PetscReal      t;
498:   PetscBool      accept;

500:   PetscFunctionBegin;
501:   PetscCall(PetscCitationsRegister(citation, &cited));

503:   for (i = 0; i < r; i++) PetscCall(VecCopy(Y[i], X[i]));

505:   PetscCall(TSGetSNES(ts, &snes));
506:   next_time_step = ts->time_step;
507:   t              = ts->ptime;
508:   accept         = PETSC_TRUE;
509:   glee->status   = TS_STEP_INCOMPLETE;

511:   for (reject = 0; reject < ts->max_reject && !ts->reason; reject++, ts->reject++) {
512:     PetscReal h = ts->time_step;
513:     PetscCall(TSPreStep(ts));

515:     for (i = 0; i < s; i++) {
516:       glee->stage_time = t + h * c[i];
517:       PetscCall(TSPreStage(ts, glee->stage_time));

519:       if (A[i * s + i] == 0) { /* Explicit stage */
520:         PetscCall(VecZeroEntries(YStage[i]));
521:         for (j = 0; j < r; j++) wr[j] = U[i * r + j];
522:         PetscCall(VecMAXPY(YStage[i], r, wr, X));
523:         for (j = 0; j < i; j++) ws[j] = h * A[i * s + j];
524:         PetscCall(VecMAXPY(YStage[i], i, ws, YdotStage));
525:       } else { /* Implicit stage */
526:         glee->scoeff = 1.0 / A[i * s + i];
527:         /* compute right-hand side */
528:         PetscCall(VecZeroEntries(W));
529:         for (j = 0; j < r; j++) wr[j] = U[i * r + j];
530:         PetscCall(VecMAXPY(W, r, wr, X));
531:         for (j = 0; j < i; j++) ws[j] = h * A[i * s + j];
532:         PetscCall(VecMAXPY(W, i, ws, YdotStage));
533:         PetscCall(VecScale(W, glee->scoeff / h));
534:         /* set initial guess */
535:         PetscCall(VecCopy(i > 0 ? YStage[i - 1] : ts->vec_sol, YStage[i]));
536:         /* solve for this stage */
537:         PetscCall(SNESSolve(snes, W, YStage[i]));
538:         PetscCall(SNESGetIterationNumber(snes, &its));
539:         PetscCall(SNESGetLinearSolveIterations(snes, &lits));
540:         ts->snes_its += its;
541:         ts->ksp_its += lits;
542:       }
543:       PetscCall(TSGetAdapt(ts, &adapt));
544:       PetscCall(TSAdaptCheckStage(adapt, ts, glee->stage_time, YStage[i], &accept));
545:       if (!accept) goto reject_step;
546:       PetscCall(TSPostStage(ts, glee->stage_time, i, YStage));
547:       PetscCall(TSComputeRHSFunction(ts, t + h * c[i], YStage[i], YdotStage[i]));
548:     }
549:     PetscCall(TSEvaluateStep(ts, tab->order, ts->vec_sol, NULL));
550:     glee->status = TS_STEP_PENDING;

552:     /* Register only the current method as a candidate because we're not supporting multiple candidates yet. */
553:     PetscCall(TSGetAdapt(ts, &adapt));
554:     PetscCall(TSAdaptCandidatesClear(adapt));
555:     PetscCall(TSAdaptCandidateAdd(adapt, tab->name, tab->order, 1, tab->ccfl, (PetscReal)tab->s, PETSC_TRUE));
556:     PetscCall(TSAdaptChoose(adapt, ts, ts->time_step, &next_scheme, &next_time_step, &accept));
557:     if (accept) {
558:       /* ignore next_scheme for now */
559:       ts->ptime += ts->time_step;
560:       ts->time_step = next_time_step;
561:       glee->status  = TS_STEP_COMPLETE;
562:       /* compute and store the global error */
563:       /* Note: this is not needed if TSAdaptGLEE is not used */
564:       PetscCall(TSGetTimeError(ts, 0, &glee->yGErr));
565:       PetscCall(PetscObjectComposedDataSetReal((PetscObject)ts->vec_sol, explicit_stage_time_id, ts->ptime));
566:       break;
567:     } else { /* Roll back the current step */
568:       for (j = 0; j < r; j++) wr[j] = F[j];
569:       PetscCall(VecMAXPY(ts->vec_sol, r, wr, X));
570:       ts->time_step = next_time_step;
571:       glee->status  = TS_STEP_INCOMPLETE;
572:     }
573:   reject_step:
574:     continue;
575:   }
576:   if (glee->status != TS_STEP_COMPLETE && !ts->reason) ts->reason = TS_DIVERGED_STEP_REJECTED;
577:   PetscFunctionReturn(PETSC_SUCCESS);
578: }

580: static PetscErrorCode TSInterpolate_GLEE(TS ts, PetscReal itime, Vec X)
581: {
582:   TS_GLEE         *glee = (TS_GLEE *)ts->data;
583:   PetscInt         s = glee->tableau->s, pinterp = glee->tableau->pinterp, i, j;
584:   PetscReal        h, tt, t;
585:   PetscScalar     *b;
586:   const PetscReal *B = glee->tableau->binterp;

588:   PetscFunctionBegin;
589:   PetscCheck(B, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "TSGLEE %s does not have an interpolation formula", glee->tableau->name);
590:   switch (glee->status) {
591:   case TS_STEP_INCOMPLETE:
592:   case TS_STEP_PENDING:
593:     h = ts->time_step;
594:     t = (itime - ts->ptime) / h;
595:     break;
596:   case TS_STEP_COMPLETE:
597:     h = ts->ptime - ts->ptime_prev;
598:     t = (itime - ts->ptime) / h + 1; /* In the interval [0,1] */
599:     break;
600:   default:
601:     SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_PLIB, "Invalid TSStepStatus");
602:   }
603:   PetscCall(PetscMalloc1(s, &b));
604:   for (i = 0; i < s; i++) b[i] = 0;
605:   for (j = 0, tt = t; j < pinterp; j++, tt *= t) {
606:     for (i = 0; i < s; i++) b[i] += h * B[i * pinterp + j] * tt;
607:   }
608:   PetscCall(VecCopy(glee->YStage[0], X));
609:   PetscCall(VecMAXPY(X, s, b, glee->YdotStage));
610:   PetscCall(PetscFree(b));
611:   PetscFunctionReturn(PETSC_SUCCESS);
612: }

614: /*------------------------------------------------------------*/
615: static PetscErrorCode TSReset_GLEE(TS ts)
616: {
617:   TS_GLEE *glee = (TS_GLEE *)ts->data;
618:   PetscInt s, r;

620:   PetscFunctionBegin;
621:   if (!glee->tableau) PetscFunctionReturn(PETSC_SUCCESS);
622:   s = glee->tableau->s;
623:   r = glee->tableau->r;
624:   PetscCall(VecDestroyVecs(r, &glee->Y));
625:   PetscCall(VecDestroyVecs(r, &glee->X));
626:   PetscCall(VecDestroyVecs(s, &glee->YStage));
627:   PetscCall(VecDestroyVecs(s, &glee->YdotStage));
628:   PetscCall(VecDestroy(&glee->Ydot));
629:   PetscCall(VecDestroy(&glee->yGErr));
630:   PetscCall(VecDestroy(&glee->W));
631:   PetscCall(PetscFree2(glee->swork, glee->rwork));
632:   PetscFunctionReturn(PETSC_SUCCESS);
633: }

635: static PetscErrorCode TSGLEEGetVecs(TS ts, DM dm, Vec *Ydot)
636: {
637:   TS_GLEE *glee = (TS_GLEE *)ts->data;

639:   PetscFunctionBegin;
640:   if (Ydot) {
641:     if (dm && dm != ts->dm) {
642:       PetscCall(DMGetNamedGlobalVector(dm, "TSGLEE_Ydot", Ydot));
643:     } else *Ydot = glee->Ydot;
644:   }
645:   PetscFunctionReturn(PETSC_SUCCESS);
646: }

648: static PetscErrorCode TSGLEERestoreVecs(TS ts, DM dm, Vec *Ydot)
649: {
650:   PetscFunctionBegin;
651:   if (Ydot) {
652:     if (dm && dm != ts->dm) PetscCall(DMRestoreNamedGlobalVector(dm, "TSGLEE_Ydot", Ydot));
653:   }
654:   PetscFunctionReturn(PETSC_SUCCESS);
655: }

657: /*
658:   This defines the nonlinear equation that is to be solved with SNES
659: */
660: static PetscErrorCode SNESTSFormFunction_GLEE(SNES snes, Vec X, Vec F, TS ts)
661: {
662:   TS_GLEE  *glee = (TS_GLEE *)ts->data;
663:   DM        dm, dmsave;
664:   Vec       Ydot;
665:   PetscReal shift = glee->scoeff / ts->time_step;

667:   PetscFunctionBegin;
668:   PetscCall(SNESGetDM(snes, &dm));
669:   PetscCall(TSGLEEGetVecs(ts, dm, &Ydot));
670:   /* Set Ydot = shift*X */
671:   PetscCall(VecCopy(X, Ydot));
672:   PetscCall(VecScale(Ydot, shift));
673:   dmsave = ts->dm;
674:   ts->dm = dm;

676:   PetscCall(TSComputeIFunction(ts, glee->stage_time, X, Ydot, F, PETSC_FALSE));

678:   ts->dm = dmsave;
679:   PetscCall(TSGLEERestoreVecs(ts, dm, &Ydot));
680:   PetscFunctionReturn(PETSC_SUCCESS);
681: }

683: static PetscErrorCode SNESTSFormJacobian_GLEE(SNES snes, Vec X, Mat A, Mat B, TS ts)
684: {
685:   TS_GLEE  *glee = (TS_GLEE *)ts->data;
686:   DM        dm, dmsave;
687:   Vec       Ydot;
688:   PetscReal shift = glee->scoeff / ts->time_step;

690:   PetscFunctionBegin;
691:   PetscCall(SNESGetDM(snes, &dm));
692:   PetscCall(TSGLEEGetVecs(ts, dm, &Ydot));
693:   /* glee->Ydot has already been computed in SNESTSFormFunction_GLEE (SNES guarantees this) */
694:   dmsave = ts->dm;
695:   ts->dm = dm;

697:   PetscCall(TSComputeIJacobian(ts, glee->stage_time, X, Ydot, shift, A, B, PETSC_FALSE));

699:   ts->dm = dmsave;
700:   PetscCall(TSGLEERestoreVecs(ts, dm, &Ydot));
701:   PetscFunctionReturn(PETSC_SUCCESS);
702: }

704: static PetscErrorCode DMCoarsenHook_TSGLEE(DM fine, DM coarse, void *ctx)
705: {
706:   PetscFunctionBegin;
707:   PetscFunctionReturn(PETSC_SUCCESS);
708: }

710: static PetscErrorCode DMRestrictHook_TSGLEE(DM fine, Mat restrct, Vec rscale, Mat inject, DM coarse, void *ctx)
711: {
712:   PetscFunctionBegin;
713:   PetscFunctionReturn(PETSC_SUCCESS);
714: }

716: static PetscErrorCode DMSubDomainHook_TSGLEE(DM dm, DM subdm, void *ctx)
717: {
718:   PetscFunctionBegin;
719:   PetscFunctionReturn(PETSC_SUCCESS);
720: }

722: static PetscErrorCode DMSubDomainRestrictHook_TSGLEE(DM dm, VecScatter gscat, VecScatter lscat, DM subdm, void *ctx)
723: {
724:   PetscFunctionBegin;
725:   PetscFunctionReturn(PETSC_SUCCESS);
726: }

728: static PetscErrorCode TSSetUp_GLEE(TS ts)
729: {
730:   TS_GLEE    *glee = (TS_GLEE *)ts->data;
731:   GLEETableau tab;
732:   PetscInt    s, r;
733:   DM          dm;

735:   PetscFunctionBegin;
736:   if (!glee->tableau) PetscCall(TSGLEESetType(ts, TSGLEEDefaultType));
737:   tab = glee->tableau;
738:   s   = tab->s;
739:   r   = tab->r;
740:   PetscCall(VecDuplicateVecs(ts->vec_sol, r, &glee->Y));
741:   PetscCall(VecDuplicateVecs(ts->vec_sol, r, &glee->X));
742:   PetscCall(VecDuplicateVecs(ts->vec_sol, s, &glee->YStage));
743:   PetscCall(VecDuplicateVecs(ts->vec_sol, s, &glee->YdotStage));
744:   PetscCall(VecDuplicate(ts->vec_sol, &glee->Ydot));
745:   PetscCall(VecDuplicate(ts->vec_sol, &glee->yGErr));
746:   PetscCall(VecZeroEntries(glee->yGErr));
747:   PetscCall(VecDuplicate(ts->vec_sol, &glee->W));
748:   PetscCall(PetscMalloc2(s, &glee->swork, r, &glee->rwork));
749:   PetscCall(TSGetDM(ts, &dm));
750:   PetscCall(DMCoarsenHookAdd(dm, DMCoarsenHook_TSGLEE, DMRestrictHook_TSGLEE, ts));
751:   PetscCall(DMSubDomainHookAdd(dm, DMSubDomainHook_TSGLEE, DMSubDomainRestrictHook_TSGLEE, ts));
752:   PetscFunctionReturn(PETSC_SUCCESS);
753: }

755: static PetscErrorCode TSStartingMethod_GLEE(TS ts)
756: {
757:   TS_GLEE    *glee = (TS_GLEE *)ts->data;
758:   GLEETableau tab  = glee->tableau;
759:   PetscInt    r    = tab->r, i;
760:   PetscReal  *S    = tab->S;

762:   PetscFunctionBegin;
763:   for (i = 0; i < r; i++) {
764:     PetscCall(VecZeroEntries(glee->Y[i]));
765:     PetscCall(VecAXPY(glee->Y[i], S[i], ts->vec_sol));
766:   }
767:   PetscFunctionReturn(PETSC_SUCCESS);
768: }

770: /*------------------------------------------------------------*/

772: static PetscErrorCode TSSetFromOptions_GLEE(TS ts, PetscOptionItems *PetscOptionsObject)
773: {
774:   char gleetype[256];

776:   PetscFunctionBegin;
777:   PetscOptionsHeadBegin(PetscOptionsObject, "GLEE ODE solver options");
778:   {
779:     GLEETableauLink link;
780:     PetscInt        count, choice;
781:     PetscBool       flg;
782:     const char    **namelist;

784:     PetscCall(PetscStrncpy(gleetype, TSGLEEDefaultType, sizeof(gleetype)));
785:     for (link = GLEETableauList, count = 0; link; link = link->next, count++);
786:     PetscCall(PetscMalloc1(count, (char ***)&namelist));
787:     for (link = GLEETableauList, count = 0; link; link = link->next, count++) namelist[count] = link->tab.name;
788:     PetscCall(PetscOptionsEList("-ts_glee_type", "Family of GLEE method", "TSGLEESetType", (const char *const *)namelist, count, gleetype, &choice, &flg));
789:     PetscCall(TSGLEESetType(ts, flg ? namelist[choice] : gleetype));
790:     PetscCall(PetscFree(namelist));
791:   }
792:   PetscOptionsHeadEnd();
793:   PetscFunctionReturn(PETSC_SUCCESS);
794: }

796: static PetscErrorCode TSView_GLEE(TS ts, PetscViewer viewer)
797: {
798:   TS_GLEE    *glee = (TS_GLEE *)ts->data;
799:   GLEETableau tab  = glee->tableau;
800:   PetscBool   iascii;

802:   PetscFunctionBegin;
803:   PetscCall(PetscObjectTypeCompare((PetscObject)viewer, PETSCVIEWERASCII, &iascii));
804:   if (iascii) {
805:     TSGLEEType gleetype;
806:     char       buf[512];
807:     PetscCall(TSGLEEGetType(ts, &gleetype));
808:     PetscCall(PetscViewerASCIIPrintf(viewer, "  GLEE type %s\n", gleetype));
809:     PetscCall(PetscFormatRealArray(buf, sizeof(buf), "% 8.6f", tab->s, tab->c));
810:     PetscCall(PetscViewerASCIIPrintf(viewer, "  Abscissa     c = %s\n", buf));
811:     /* Note: print out r as well */
812:   }
813:   PetscFunctionReturn(PETSC_SUCCESS);
814: }

816: static PetscErrorCode TSLoad_GLEE(TS ts, PetscViewer viewer)
817: {
818:   SNES    snes;
819:   TSAdapt tsadapt;

821:   PetscFunctionBegin;
822:   PetscCall(TSGetAdapt(ts, &tsadapt));
823:   PetscCall(TSAdaptLoad(tsadapt, viewer));
824:   PetscCall(TSGetSNES(ts, &snes));
825:   PetscCall(SNESLoad(snes, viewer));
826:   /* function and Jacobian context for SNES when used with TS is always ts object */
827:   PetscCall(SNESSetFunction(snes, NULL, NULL, ts));
828:   PetscCall(SNESSetJacobian(snes, NULL, NULL, NULL, ts));
829:   PetscFunctionReturn(PETSC_SUCCESS);
830: }

832: /*@C
833:   TSGLEESetType - Set the type of `TSGLEE` scheme

835:   Logically Collective

837:   Input Parameters:
838: + ts       - timestepping context
839: - gleetype - type of `TSGLEE` scheme

841:   Level: intermediate

843: .seealso: [](ch_ts), `TSGLEEGetType()`, `TSGLEE`
844: @*/
845: PetscErrorCode TSGLEESetType(TS ts, TSGLEEType gleetype)
846: {
847:   PetscFunctionBegin;
849:   PetscAssertPointer(gleetype, 2);
850:   PetscTryMethod(ts, "TSGLEESetType_C", (TS, TSGLEEType), (ts, gleetype));
851:   PetscFunctionReturn(PETSC_SUCCESS);
852: }

854: /*@C
855:   TSGLEEGetType - Get the type of `TSGLEE` scheme

857:   Logically Collective

859:   Input Parameter:
860: . ts - timestepping context

862:   Output Parameter:
863: . gleetype - type of `TSGLEE` scheme

865:   Level: intermediate

867: .seealso: [](ch_ts), `TSGLEE`, `TSGLEESetType()`
868: @*/
869: PetscErrorCode TSGLEEGetType(TS ts, TSGLEEType *gleetype)
870: {
871:   PetscFunctionBegin;
873:   PetscUseMethod(ts, "TSGLEEGetType_C", (TS, TSGLEEType *), (ts, gleetype));
874:   PetscFunctionReturn(PETSC_SUCCESS);
875: }

877: static PetscErrorCode TSGLEEGetType_GLEE(TS ts, TSGLEEType *gleetype)
878: {
879:   TS_GLEE *glee = (TS_GLEE *)ts->data;

881:   PetscFunctionBegin;
882:   if (!glee->tableau) PetscCall(TSGLEESetType(ts, TSGLEEDefaultType));
883:   *gleetype = glee->tableau->name;
884:   PetscFunctionReturn(PETSC_SUCCESS);
885: }
886: static PetscErrorCode TSGLEESetType_GLEE(TS ts, TSGLEEType gleetype)
887: {
888:   TS_GLEE        *glee = (TS_GLEE *)ts->data;
889:   PetscBool       match;
890:   GLEETableauLink link;

892:   PetscFunctionBegin;
893:   if (glee->tableau) {
894:     PetscCall(PetscStrcmp(glee->tableau->name, gleetype, &match));
895:     if (match) PetscFunctionReturn(PETSC_SUCCESS);
896:   }
897:   for (link = GLEETableauList; link; link = link->next) {
898:     PetscCall(PetscStrcmp(link->tab.name, gleetype, &match));
899:     if (match) {
900:       PetscCall(TSReset_GLEE(ts));
901:       glee->tableau = &link->tab;
902:       PetscFunctionReturn(PETSC_SUCCESS);
903:     }
904:   }
905:   SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_UNKNOWN_TYPE, "Could not find '%s'", gleetype);
906: }

908: static PetscErrorCode TSGetStages_GLEE(TS ts, PetscInt *ns, Vec **Y)
909: {
910:   TS_GLEE *glee = (TS_GLEE *)ts->data;

912:   PetscFunctionBegin;
913:   if (ns) *ns = glee->tableau->s;
914:   if (Y) *Y = glee->YStage;
915:   PetscFunctionReturn(PETSC_SUCCESS);
916: }

918: static PetscErrorCode TSGetSolutionComponents_GLEE(TS ts, PetscInt *n, Vec *Y)
919: {
920:   TS_GLEE    *glee = (TS_GLEE *)ts->data;
921:   GLEETableau tab  = glee->tableau;

923:   PetscFunctionBegin;
924:   if (!Y) *n = tab->r;
925:   else {
926:     if ((*n >= 0) && (*n < tab->r)) {
927:       PetscCall(VecCopy(glee->Y[*n], *Y));
928:     } else SETERRQ(PetscObjectComm((PetscObject)ts), PETSC_ERR_ARG_OUTOFRANGE, "Second argument (%" PetscInt_FMT ") out of range[0,%" PetscInt_FMT "].", *n, tab->r - 1);
929:   }
930:   PetscFunctionReturn(PETSC_SUCCESS);
931: }

933: static PetscErrorCode TSGetAuxSolution_GLEE(TS ts, Vec *X)
934: {
935:   TS_GLEE     *glee = (TS_GLEE *)ts->data;
936:   GLEETableau  tab  = glee->tableau;
937:   PetscReal   *F    = tab->Fembed;
938:   PetscInt     r    = tab->r;
939:   Vec         *Y    = glee->Y;
940:   PetscScalar *wr   = glee->rwork;
941:   PetscInt     i;

943:   PetscFunctionBegin;
944:   PetscCall(VecZeroEntries(*X));
945:   for (i = 0; i < r; i++) wr[i] = F[i];
946:   PetscCall(VecMAXPY(*X, r, wr, Y));
947:   PetscFunctionReturn(PETSC_SUCCESS);
948: }

950: static PetscErrorCode TSGetTimeError_GLEE(TS ts, PetscInt n, Vec *X)
951: {
952:   TS_GLEE     *glee = (TS_GLEE *)ts->data;
953:   GLEETableau  tab  = glee->tableau;
954:   PetscReal   *F    = tab->Ferror;
955:   PetscInt     r    = tab->r;
956:   Vec         *Y    = glee->Y;
957:   PetscScalar *wr   = glee->rwork;
958:   PetscInt     i;

960:   PetscFunctionBegin;
961:   PetscCall(VecZeroEntries(*X));
962:   if (n == 0) {
963:     for (i = 0; i < r; i++) wr[i] = F[i];
964:     PetscCall(VecMAXPY(*X, r, wr, Y));
965:   } else if (n == -1) {
966:     *X = glee->yGErr;
967:   }
968:   PetscFunctionReturn(PETSC_SUCCESS);
969: }

971: static PetscErrorCode TSSetTimeError_GLEE(TS ts, Vec X)
972: {
973:   TS_GLEE    *glee = (TS_GLEE *)ts->data;
974:   GLEETableau tab  = glee->tableau;
975:   PetscReal  *S    = tab->Serror;
976:   PetscInt    r    = tab->r, i;
977:   Vec        *Y    = glee->Y;

979:   PetscFunctionBegin;
980:   PetscCheck(r == 2, PetscObjectComm((PetscObject)ts), PETSC_ERR_SUP, "TSSetTimeError_GLEE not supported for '%s' with r=%" PetscInt_FMT ".", tab->name, tab->r);
981:   for (i = 1; i < r; i++) {
982:     PetscCall(VecCopy(ts->vec_sol, Y[i]));
983:     PetscCall(VecAXPBY(Y[i], S[0], S[1], X));
984:     PetscCall(VecCopy(X, glee->yGErr));
985:   }
986:   PetscFunctionReturn(PETSC_SUCCESS);
987: }

989: static PetscErrorCode TSDestroy_GLEE(TS ts)
990: {
991:   PetscFunctionBegin;
992:   PetscCall(TSReset_GLEE(ts));
993:   if (ts->dm) {
994:     PetscCall(DMCoarsenHookRemove(ts->dm, DMCoarsenHook_TSGLEE, DMRestrictHook_TSGLEE, ts));
995:     PetscCall(DMSubDomainHookRemove(ts->dm, DMSubDomainHook_TSGLEE, DMSubDomainRestrictHook_TSGLEE, ts));
996:   }
997:   PetscCall(PetscFree(ts->data));
998:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLEEGetType_C", NULL));
999:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLEESetType_C", NULL));
1000:   PetscFunctionReturn(PETSC_SUCCESS);
1001: }

1003: /* ------------------------------------------------------------ */
1004: /*MC
1005:       TSGLEE - ODE and DAE solver using General Linear with Error Estimation schemes

1007:   The user should provide the right-hand side of the equation using `TSSetRHSFunction()`.

1009:   Level: beginner

1011:   Note:
1012:   The default is `TSGLEE35`, it can be changed with `TSGLEESetType()` or -ts_glee_type

1014: .seealso: [](ch_ts), `TSCreate()`, `TS`, `TSSetType()`, `TSGLEESetType()`, `TSGLEEGetType()`,
1015:           `TSGLEE23`, `TTSGLEE24`, `TSGLEE35`, `TSGLEE25I`, `TSGLEEEXRK2A`,
1016:           `TSGLEERK32G1`, `TSGLEERK285EX`, `TSGLEEType`, `TSGLEERegister()`, `TSType`
1017: M*/
1018: PETSC_EXTERN PetscErrorCode TSCreate_GLEE(TS ts)
1019: {
1020:   TS_GLEE *th;

1022:   PetscFunctionBegin;
1023:   PetscCall(TSGLEEInitializePackage());

1025:   ts->ops->reset                 = TSReset_GLEE;
1026:   ts->ops->destroy               = TSDestroy_GLEE;
1027:   ts->ops->view                  = TSView_GLEE;
1028:   ts->ops->load                  = TSLoad_GLEE;
1029:   ts->ops->setup                 = TSSetUp_GLEE;
1030:   ts->ops->step                  = TSStep_GLEE;
1031:   ts->ops->interpolate           = TSInterpolate_GLEE;
1032:   ts->ops->evaluatestep          = TSEvaluateStep_GLEE;
1033:   ts->ops->setfromoptions        = TSSetFromOptions_GLEE;
1034:   ts->ops->getstages             = TSGetStages_GLEE;
1035:   ts->ops->snesfunction          = SNESTSFormFunction_GLEE;
1036:   ts->ops->snesjacobian          = SNESTSFormJacobian_GLEE;
1037:   ts->ops->getsolutioncomponents = TSGetSolutionComponents_GLEE;
1038:   ts->ops->getauxsolution        = TSGetAuxSolution_GLEE;
1039:   ts->ops->gettimeerror          = TSGetTimeError_GLEE;
1040:   ts->ops->settimeerror          = TSSetTimeError_GLEE;
1041:   ts->ops->startingmethod        = TSStartingMethod_GLEE;
1042:   ts->default_adapt_type         = TSADAPTGLEE;

1044:   ts->usessnes = PETSC_TRUE;

1046:   PetscCall(PetscNew(&th));
1047:   ts->data = (void *)th;

1049:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLEEGetType_C", TSGLEEGetType_GLEE));
1050:   PetscCall(PetscObjectComposeFunction((PetscObject)ts, "TSGLEESetType_C", TSGLEESetType_GLEE));
1051:   PetscFunctionReturn(PETSC_SUCCESS);
1052: }